ЁЯУв Too many exams? DonтАЩt know which one suits you best? Book Your Free Expert ЁЯСЙ call Now!

    Question

    Find the reciprocal of the complex number z = 9 тАУ 4i.

    A 9/97 тАУ 4i/97 Correct Answer Incorrect Answer
    B 4/97 + 9i/97 Correct Answer Incorrect Answer
    C 4/97 тАУ 9i/97 Correct Answer Incorrect Answer
    D 9/97 + 4i/97 Correct Answer Incorrect Answer

    Solution

    We are given the complex number: z = 9 тАУ 4i We are to find its reciprocal , i.e., 1 / z To find the reciprocal of a complex number, multiply numerator and denominator by the conjugate of the denominator: 1 / (9 тАУ 4i) ├Ч (9 + 4i) / (9 + 4i) = (9 + 4i) / [(9 тАУ 4i)(9 + 4i)] = (9 + 4i) / (9┬▓ + 4┬▓) = (9 + 4i) / (81 + 16) = (9 + 4i) / 97 So: 1 / z = 9/97 + 4i/97

    Practice Next
    More Quant Miscellaneous Questions

    Relevant for Exams:

    ask-question